Mathematical Formulation
A phenomenological framework describing the non-linear and asymmetric recovery of glass-forming systems uses a set of internal variables to track structural state changes. This formulation, known as the Kovacs-Aklonis-Hutchinson-Ramos model, accounts for the structural relaxation times of amorphous materials during temperature sweeps. The framework uses a distribution of relaxation times to capture complex material histories.
Microstructural Parameter
The calculation of the structural state involves both temperature and structural deviation. In the Kovacs-Aklonis-Hutchinson-Ramos model, a parameter defines how these relaxation times depend on the instantaneous volume of the glass. This coupling enables the simulation of structural transitions.
Thermal Response
Simulating rapid cooling and heating cycles demonstrates the complex behavior of polymer networks. The Kovacs-Aklonis-Hutchinson-Ramos model accurately describes the asymmetry of recovery where expansion and contraction follow different paths. These simulated curves show why glasses undergo structural aging at varying rates depending on the path taken, allowing engineers to predict long term dimensions in molded optical parts.
Memory Phenomenon
A complex temperature history can induce a transient reversal in the direction of structural recovery. Predicting this behavior requires the Kovacs-Aklonis-Hutchinson-Ramos model to calculate how the different relaxation mechanisms interact. The model reveals how intermediate annealing steps change the volumetric stability of high precision polymer lenses.
